
While, as we have discussed in detail, we are driven by the edge and higher order correlations centered approach, the node based one is still relevant. Therefore, the exploration of the capabilities of the (scalar curvature) Yamabe flow is a natural and interesting venue of research.

Of particular interest is the exploration of flows in the study of the long-time evolution of (hyper-)networks [1]}. To this end, flows derived from all the types of curvature herein should be examined.

Experiments with curvature-driven triangulations of manifolds and their sampling, especially for such manifolds as arising in Deep Learning (see references mentioned above) should definitely represent a future goal.

One should try other embedding techniques than the one used herein, for instance the so called local linear embedding [2]}.

Besides the kernel embedding method embraced in the present paper, one should explore another, and perhaps better established approach, that is the one using the eigenvectors and eigenfunctions of the Laplacian for emebedding and sampling, where the classical graph Laplacian is replaced by the Bochner and rough ones.
Furthermore, given that they exist for each and every dimension up to the maximal one, they suggest themselves as a potentially powerful method of studying hypernetworks/complexes at many scales.

The stronger results connecting Forman curvatures of discretizations, namely the convergence of the said curvatures to their manifold counterparts, as well as of the associated Laplacians to the smooth ones, is a goal that definitely should be pursued.

